Jack Tibbetts, a member of the Santa Rosa, Calif., city council, knew he had a problem. It was early 2018, and he’d started getting calls from constituents at opposite ends of the political spectrum. The common thread: cellular antennas going up next to their homes, causing concerns over property values and health.

The weight of evidence suggests that if radio-frequency emissions have any effect on humans at all, it is, according to the World Health Organization, about on par with other “possibly carcinogenic” substances,...